#### Vol. 311, No. 2, 2021

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Spinoriality of orthogonal representations of $\mathrm{GL}_n(\mathbb{F}_q)$

### Rohit Joshi and Steven Spallone

Vol. 311 (2021), No. 2, 369–383
##### Abstract

We determine which orthogonal representations $V$ of ${GL}_{n}\left({\mathbb{𝔽}}_{q}\right)$ lift to the double cover $Pin\left(V\right)$ of the orthogonal group $O\left(V\right)$. We cover all $n\ge 1$ and prime powers $q$, except for $\left(n,q\right)=\left(3,4\right)$.

##### Keywords
orthogonal representations, spinoriality, finite groups of Lie type
Primary: 20G05
Secondary: 20G40